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As far as I can tell; you typed it in there. :)
It's on the website where I found this openstudy group. I never answered it. It says that's the answer and I'm a bit confused.
You have 2 numbers that are the same (2x+7) and (2x+7); so factor those out and your left with: (2x+7) (9x^2-12x) does this make sense? Now, we can factor (9x^2 -12x) even further to get: 3x (x-4) ; it should be: (3x) (2x+7) (x-4). It would be a typo :)
ack!! my mistake 3x(3x-4) is correct... do you know why?
No, I don't know why. xD I have a math 11 test tomorrow and I'm a bit nervous. I can't get the hang of this stuff. :/ Mind explaining?
do you understand the first step....how to factor out (2x+7) and get left with (9x^2 -12x)? It is the opposite of distirbuting...
The question is 9x^2(2x+7)-12x(2x+7) and I know that theres a 3x in each term and a (2x+7) so you can factor those out right? So on the site it says it equals 3x(2x+7)(3x-4) and I understand how I got the 3x(2x+7) because both terms have it, but I'm so lost as to where the 3x-4 came up.
lets take it step by step and you will see where it comes from...fair enough?
9x^2(2x+7)-12x(2x+7) has a common factor that is blaringly obvious. It is (2x+7) right? just let me know if this is correct....
Yes, but doesn't it have 3x as well?
3x doesnt matter yet; it will come, but not yet. lets clean it up some first ok?
kk, so yes, 2x+7
when we factor out (2x+7) are we left with: (2x+7) (9x^2 -12x) ? yes or no...
think of (2x+7) call it A if you have to..
yes, we're left with it.
sorry i'm talkign long to reply. keep pressing enter instead of post.
its ok... Now we can factor (9x^2 -12x). Do you see how we could do that?
Oh wait! So, you can take out a 3 because of 9 and 12, and you can also take out an x, hence 3x, and you can get a 4 because 3X4 = 12.
you are brilliant :)
So once we get that we just put the 2x+7 back in?
And our 3x would go in front.
3x(3x - 4) = 9x^2 -12x right?
but yes, you can put the numbers back in whatever order you feel comfortable with.
So that's why there was a 4. I was confused about that but now I get it, because of the 3-4, 3x4= 12. Makes so much more sense now.
Just remember to take things step-by-step and it should all work out :)
I'm still bad at this stuff, though. I understand that question, but there's like 4 different types of facorting we're doing in class and I get confused when I'm doing problems because I'm not sure which one I'm supposed to use.
I hate the way they teach factoring in school. Because there is only one method that you actually use.. it is to "un" distribute or take apart; what was already put together.
& my math teacher picks favorites, if you're not up there in your math grades then he'll get mad. It's really annoying. I failed my past two math tests. I had 88 on my first test, but when he started teaching I dropped down to half that mark, to like 44. Tomorrow's test is kinda crucial.
what factoring methods do you need help with?
I'm strong in every other subject besides math. Anyways, care to help me with a couple more problems?
I'll list a problem I was having trouble with today. One second, I'll find it in my book.
x^2+8x+12 x^2+3x-18 and it's supposed to be over each other.
The top part = (x+2)(x+3) right?
glorified fractions is all that is. The equation gives you clues as to what to do. Do you see the "sign" of the last term?
What sign? I'm not sure what you mean by that, sorry.
(+12) OR (-18) the last term is gotten by multipying 2 numbers together. What combination of "signs" when multiplied give you a (+) answer? What combination of "signs" when multiplied give you a (-) answer? Can you tell me?
two positives = positive, two negatives = positive, and a - and a + = a -, right?
thats right. So the last term gives us a clue about our middle term. Becuase the middle term takes those same 2 numbers and adds them together. Lets focus on the top: +8 +12. we need 2 numbers that are either (-)(-) or (+)(+) to get the (+12) right? and they need to add together to get a (+) for the middle term (+8). Does this make sense?
Yeah that makes sense, we're trying to get a LCD?
2 and 6?
we will soon enough; but lets take it step by step. We can start to set up our answer like this: Good now... (x 2 ) (x 6 ) what "sign" do we need to use to fill this in? to get a (+12) and a (+8)
Yes, (x+2) (x+8) is the answer for the top; store it away somewhere where it wont get broken...
opps... make that (x+2)(x+6) and feel free to correct me :)
That's the answer for the top? Don't the 6 break down to a 3? Or we can't do that because we're only going half of 12?
there is nothing that x and 6 have in common so it is as far as it will go. to double check, multiply them back together.
x^2 +3x -18 the last term tells us what signs we need to use. and the middle term tells us which of those signs gets the bigger number. Does that make sense?
what makes a (-) when multiplied together?
+ and -
I don't know what you mean by which sign gets the bigger number, though.
good; then its our only option: (x+ )(x- ) is what we are dealt. now find 2 numbers that multiply to 18 and "subtract" to get 3. Do you see why we need the (+)number to be bigger than the (-)number to get (+3)?
I'm a bit confused.
the numbers are gonna be 6 and 3... to equal 18 right? -6 +3 = -3 +6 -3 = +3 do you see it?
I thought we were trying to equal 18? Not - and +3?
ok...we can do that as well; what are the factors of 18 that subtract to get (+3) for a middle term? 1 and 18 2 and 9 3 and 6 thats it... right?
one number has to be (-) and the other number has to (+) In order to get the (+3) for the middle term, the largest number has to be (+) such as: +6 -3 = +3 and +6 times -3 equals -18 does this make sense?
yes, it does!
then we can fill in our stuff now: (x +6) (x -3) is our answer. for the bottom. Can we cross anything out from top to bottom that are alike?
Good, and we are left with: (x+2)(x+6) (x+2) ---------- = ----- (x+6)(x-3) (x-3)
so then it's gonna be x+2 over x+3
thats what I had written down on paper, typo on here. lol.
i wish I had time for more, but my macroeconomics class is starting and running for the next 2 hours. You can do this, it is really stuff you already know :)
Thanks for your help, and perfect timing. I have to go right now too.